System and Method for Probabilistic Multi-Robot Positioning

ABSTRACT

A system for estimating a pose of a robot includes a particle filter to track the pose of the robot using particles that defining a probability of pose of the robot and a particle tuner to update the particles of the robot based on particles of neighboring robot. Upon receiving data indicative of relative pose between a pose of the robot and a pose of a neighboring robot, and particles of the neighboring robot, the particle tuner pairs an arbitrarily sampled particle of the robot with an arbitrarily sampled particle of the neighboring robot, determines a weight of the paired particles in reverse proportion to an error between a relative pose defined by the paired particles and the relative pose between the robot and the neighboring robot, and updates the particles of the robot in accordance to the weights of corresponding paired particles.

TECHNICAL FIELD

The invention relates generally to a mobile robot, and, moreparticularly, to probabilistic multi-robot positioning.

BACKGROUND

One of the most essential prerequisites behind a successful taskexecution of a team of robots is to accurately estimate and trackrobots' poses. A general problem of robot positioning includesestimating pose of a robot based on measurements from sensors indicativeof motion of the robot, such as odometry, sensors providing environmentmeasurements, such as visual camera, depth camera, lidar, and, possibly,some external information. The robot positioning is at the core ofnearly all robotics applications.

Positioning of a single robot has received tremendous attention withnumerous systems, algorithms and use cases. Recently, the scenario wheremultiple robots collaboratively perform a task started to gain interest.Positioning of robots in a multi-robot system is advantageous. A naïveapproach in positioning of multiple robots is to have each robot performsingle-robot positioning. However, since the robots are already enabledto exchange information with the aim to collaboratively execute sometask, why not then have them collaboratively perform positioning aswell. That is, each robot may position itself using not only its ownodometry and environment measurements, but also information receivedfrom other robots. The advantages of this approach may include moreaccurate positioning, faster convergence of estimation, and robustness.

Some methods in multi-robot positioning aim to reduce odometry errorsusing robot cooperation. A common framework includes instructing a setof robots to be stationary while the remaining robots move so that therobots in one group measure the motion of the robots in the other groupand refine odometry measurements. However, those methods do not fuseodometry with environment measurements, which can be a limitation. Inaddition, the error in the refined odometry estimates still accumulatesover time, which eventually leads to incorrect pose estimates.

In other cooperative positioning methods, robots exchange allmeasurements they have collected between their two consecutiverendezvous. Those measurements are usually odometry and laser scans. Onedrawback of this approach is an excessive communication bandwidthrequired to support exchange of huge amount of data. In addition, robotsneed to store a large amount of data, which requires large memorystorage.

Some methods, e.g., a method described by Fox et al. in “A ProbabilisticApproach to Collaborative Multi-Robot Localization” a robot infers itspose probabilistically by fusing its own odometry and environmentmeasurements with the relative pose measurements and pose particles ofthe other robot. The robots exchange pose particles and perform relativepose measurements at their random rendezvous. The information fusion isdone within the Bayesian inference framework and uses density trees toestimate robot's pose from its particles. However, a complexity of thismethod is higher than a complexity of a single-robot positioning.

To reduce complexity of density trees based position estimation, othermethods use different particle updating scheme in lieu of using thedensity trees. For example, a method of Prorok et al. described in “Areciprocal sampling algorithm for lightweight distributed multi-robotlocalization” uses the weight computation of the particles that requiresevaluating relative pose distribution for all pairs of particles fromthe two robots involved in rendezvous. However, computational complexityof this method is O(K²), where K is the number of particles. Anothermethod of Prorok described in “Low-cost collaborative localization forlarge-scale multi-robot systems” reduces computational complexity toO(KS) by clustering K particles into S clusters. However, thiscomputational complexity is still more than desired. In addition, thismethod may fail to provide performance guaranties of probabilistic poseestimation.

SUMMARY

It is an objective of some embodiments to estimate a pose of a robotprobabilistically using a particle filter. Particle filter represents apose of a robot using a set of particles. The pose of a robot includesone or combination of location and orientation of the robot. Eachparticle defines a probability of a value of the current pose of therobot.

It is another objective of some embodiments to disclose a probabilisticmulti-robot positioning system and method wherein robots exchange theirparticles upon a rendezvous. Notably, this approach does not require rawmeasurements of the sensors of each robot to be stored and exchanged ata rendezvous. Advantageously, each robot can fuse measurements of itscorresponding sensor as soon as it gets them into updated particles thatrepresent its pose. At the rendezvous, robots exchange particles leadingto a relatively mild requirement on communication bandwidth size. Inaddition, this approach allows to establish connection only when therobots come in proximity, e.g., in line of sight of each other. Thisallows to reduce a requirement on communication coverage that can beachieved with a low power transceiver, such as those implementingBluetooth standard.

It is another objective of some embodiments to provide such aprobabilistic multi-robot positioning method that reduce a computationalcomplexity, while ensuring performance guarantees provided byprobabilistic estimation.

Some embodiments are based on realization that a particle filter solvesa Bayesian inference problem, thus the multi-robot pose fusion shouldalso follow the principles of Bayesian inference to guarantee theperformance of the particle filter. However, the comparison of particlesof different robots is pairwise, i.e., particles are grouped in pairsand two particles of each pair are compared with each other to update apose of a robot. However, when pairing the particles is deterministic,such a pairing can undermine performance guaranties provided by Bayesianinference.

For example, all particles of one robot can be compared with allparticles of another robot. Such an exhaustive pairing is deterministic,but accidently follows the principles of Bayesian inference when allinformation of hypotheses is available for probability estimation.However, such a comparison results in computational complexity O(K²),where K is the number of particles. A deterministic attempt to deviatefrom exhaustive pairing violates the principles of Bayesian inference.For example, ad-hoc clustering and comparison of particles of eachcluster can reduce the computational complexity, but violates theprinciples of Bayesian inference, because clustering is deterministic.

Some embodiments are based on realization that random pairing ofparticles of different robots during probabilistic multi-robotpositioning can reduce computational complexity to O(K), where K is thenumber of randomly selected pairs of particles while ensuring theprobabilistic guarantees of particle filter. Indeed, random pairing isprobabilistic and follows the principles of Bayesian inference toguarantee performance of the particle filter. In addition, randompairing is also simple, computationally efficient, and suitable forparallel computing.

To that end, some embodiments, upon rendezvous of a robot with anotherneighbor robot, compare arbitrarily paired particles of the robots toupdate the weights of the particles and ultimately the pose of therobot. As used herein, arbitrarily paired particles are sampledarbitrarily, i.e., not deterministically. Such an arbitrarily paring canbe implemented using any random and/or a pseudo-random generatorconfigured to select numbers from a set of numbers with equalprobability, such that any number is equally likely to be selected fromthe set. In different implementations, particles are sampled uniformlyrandomly or non-uniformly randomly according to weights of the particle,such as a particle with a larger weight is more likely to be sampledthan a particle with a smaller weight.

Accordingly, one embodiment discloses a system for estimating a pose ofa robot, wherein the pose includes one or combination of a location ofthe robot and an orientation of the robot. The system includes an inputinterface configured to receive data indicative of a value of a relativepose between a current pose of the robot and a current pose of aneighboring robot, and indicative of values of particles of theneighboring robot, each particle of the neighboring robot defines aprobability of a value of the current pose of the neighboring robot; amemory configured to store values of particles of the robot, eachparticle of the robot defines a probability of a value of the currentpose of the robot, and store executable components including a particlefilter configured to track the pose of the robot using a set ofparticles, each particle defines a probability of a value of the currentpose of the robot; a particle tuner configured to pair an arbitrarilysampled particle of the robot with an arbitrarily sampled particle ofthe neighboring robot, determine a weight of the paired particles inreverse proportion to an error between a relative pose defined by thepaired particles and the relative pose between the robot and theneighboring robot, and update the particles of the robot in accordanceto the weights of corresponding paired particles; a processor configuredto track, in response to a change of the pose of the robot, the pose ofthe robot using the particle filter, and to update, in response toreceiving the data, the particles of the particle filter using theparticle turner; and an output interface configured to output thecurrent pose of the robot.

Another embodiment discloses a method for estimating a pose of a robot,wherein the pose includes one or combination of a location of the robotand an orientation of the robot, wherein the method uses a processorcoupled with stored instructions implementing the method, wherein theinstructions, when executed by the processor carry out steps of themethod, includes receiving data indicative of a value of a relative posebetween a current pose of the robot and a current pose of a neighboringrobot, and indicative of values of particles of the neighboring robot,each particle of the neighboring robot defines a probability of a valueof the current pose of the neighboring robot; tracking the pose of therobot using a set of particles, each particle defines a probability of avalue of the current pose of the robot; pairing an arbitrarily sampledparticle of the robot with an arbitrarily sampled particle of theneighboring robot, determining a weight of the paired particles inreverse proportion to an error between a relative pose defined by thepaired particles and the relative pose between the robot and theneighboring robot, and updating the particles of the robot in accordanceto the weights of corresponding paired particles.

Yet another embodiment discloses a non-transitory computer readablestorage medium embodied thereon a program executable by a processor forperforming a method, the method includes receiving data indicative of avalue of a relative pose between a current pose of the robot and acurrent pose of a neighboring robot, and indicative of values ofparticles of the neighboring robot, each particle of the neighboringrobot defines a probability of a value of the current pose of theneighboring robot; tracking the pose of the robot using a set ofparticles, each particle defines a probability of a value of the currentpose of the robot; pairing an arbitrarily sampled particle of the robotwith an arbitrarily sampled particle of the neighboring robot,determining a weight of the paired particles in reverse proportion to anerror between a relative pose defined by the paired particles and therelative pose between the robot and the neighboring robot, and updatingthe particles of the robot in accordance to the weights of correspondingpaired particles.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a schematic illustrating a scenario where multiple robotstravel in an indoor area to perform multi-robot positioning according tosome embodiments.

FIG. 1B shows a schematic of a robot utilizing cooperative robotlocalization using principles of some embodiments.

FIG. 1C shows a schematic of various components of the robot of FIG. 1B.

FIG. 1D shows a block diagram of a system 100 for estimating a pose of arobot in accordance with some embodiments.

FIG. 2A is an illustration of a pose of a robot in a reference systemused by some embodiments.

FIG. 2B is an example of an occupancy grid map used by some embodiments.

FIG. 3 shows a block diagram of a single robot pose estimation used bysome embodiments.

FIG. 4A is an illustration of particle cloud in a reference system ofFIG. 2A.

FIG. 4B is an illustration of particle cloud in an area according tosome embodiments.

FIG. 5A is a schematic illustrating a rendezvous of two robots in oneembodiment.

FIG. 5B is a schematic of a relative pose between two robots used bysome embodiments.

FIG. 6A is a principle block diagram of a cooperative localizationpipeline used by some embodiments.

FIG. 6B is a principle block diagram of information fusion performed bya particle tuner according to some embodiments.

FIG. 7 is a pseudo-code of the cooperative positioning used by oneembodiment.

FIG. 8A is a block diagram of a method for computing a weighted particlepair according to some embodiments.

FIG. 8B is a block diagram of a method used by some embodiments forupdating particles based on a weighted pair of pose particles generatedas shown in FIG. 8A.

FIG. 9A is a block diagram of pseudo-random particle sampling used bysome embodiments to implement particle sampling for a given discretedistribution z.

FIG. 9B is a block diagram of pseudo-random number generation used byone embodiment.

FIG. 10 shows a block diagram of a positioning system of a robotaccording to some embodiments.

DETAILED DESCRIPTION

FIG. 1A shows a schematic illustrating a scenario where multiple robotstravel in an indoor area to perform multi-robot positioning according tosome embodiments. In one embodiment, 2D occupancy grid map is knownand/or made available to the robots. Additionally, or alternatively,some embodiments perform simultaneous localization and mapping (SLAM) byconstructing or updating a map of an unknown environment whilesimultaneously keeping track of robot's poses.

In an example shown in FIG. 1A, three robots 121, 122 and 123 are incommon area 110 and cooperatively execute a certain task. One of themain prerequisites for a successful task execution is to enable robotsthe ability to localize themselves in the area. A naive approach is tolet each robot localize itself using one of many single-robotlocalization algorithms from prior art. However, robots may cooperatewhile performing localization with the potential benefit of obtainingmore accurate location estimates. To that end, some embodiments disclosemulti-robot positioning for cooperative robot localization.

FIG. 1B shows a schematic of a robot utilizing cooperative robotlocalization using principles of some embodiments. FIG. 1C shows aschematic of various components of the robot of FIG. 1B. A robot is afully or partially autonomous entity containing motor 106 so that it canautonomously move in an area, set of sensors 102, 103, 104, and 105 totake a variety of measurements, memory 140 to store measurements andother quantities, processor 120 to execute a variety of algorithms,transceiver 126, i.e., a receiver and a transmitter, to communicate withother robots and devices, and a battery 129 which provides electricpower to the robot and all its devices. The robot may also includeequipment 128, e.g., a gripper, for performing various tasks of therobot.

For example, a robot is equipped with a sensor for environment sensing,such as a low-cost structured light sensor, and a sensor for recordingrobot's motions, such as odometric sensors. To enable cooperation,robots need to be able to detect the presence of other robots. Thiscould be achieved in multiple ways. For example, in one scenario, afacial of a robot is marked with visible markings, while the other robotis equipped with a visual camera to detect the presence of thecheckerboard and measure the relative pose between robots (i.e.,relative range, bearing and heading).

The robots are configured to move in an area, either by random wander oraccording to some instructions, and occasionally come relatively closeto each other. Once the rendezvous is detected by one or both robots,the robots exchange a relatively small amount of information via awireless communication link. Each robot fuses the received informationwith its own information locally, using its own computational resources.In other words, the information fusion happens at each robotindependently, so that a central server is not needed.

More specifically, each robot traveling in an area localizes itself inthe map of that area using measurements from environment and motionsensing. The location estimate is obtained using a conventionalsingle-robot PF-based positioning and represented with a certain numberof pose particles. Upon the rendezvous, the two robots exchange theirparticles. This is in contrast with other multi-robot SLAM, where robotsexchange all environment and motion measurements collected between twoconsecutive rendezvous events. In addition to particles, the robotmeasuring the relative pose between robots sends that measurement to theother robot. Each robot then fuses particles representing its pose priorto the rendezvous with the particles received from the other robot andrelative pose measurement between the two robots. The result of theinformation fusion done locally on each robot is a set of updated poseparticles. The robots then continue to travel in the area and performpose estimation on their own until they meet again.

Some embodiments, upon rendezvous of a robot with another neighborrobot, compare arbitrarily paired particles of the robots to update theweights of the particles and ultimately the pose of the robot. As usedherein, arbitrarily paired particles are sampled arbitrarily, i.e., notdeterministically. Such an arbitrarily paring can be implemented usingany random and/or a pseudo-random generator configured to select numbersfrom a set of numbers with equal probability, such that any number isequally likely to be selected from the set. In differentimplementations, particles are sampled uniformly randomly ornon-uniformly randomly according to weights of the particle, such as aparticle with a larger weight is more likely to be sampled than aparticle with a smaller weight.

FIG. 1D shows a block diagram of a system 100 for estimating a pose of arobot in accordance with some embodiments. As used herein, the poseincludes one or combination of a location of the robot and anorientation of the robot. The system 100 implements a probabilisticmulti-robot positioning method that reduce a computational complexity,while ensuring performance guarantees provided by probabilisticestimation.

The system 100 includes a processor 120 configured to execute storedinstructions, as well as a memory 140 that stores instructions that areexecutable by the processor. The processor 120 can be a single coreprocessor, a multi-core processor, a computing cluster, or any number ofother configurations. The memory 140 can include random access memory(RAM), read only memory (ROM), flash memory, or any other suitablememory systems. The processor 120 is connected through a bus 106 to oneor more input and output devices. These instructions implement a methodfor probabilistic multi-robot positioning.

To that end, the system 100 includes a particle filter 131 configured totrack the pose of the robot using a set of particles. Each particledefines a probability of a value of the current pose of the robot. Theparticles can be determined and/or updated using measurements of thesensors of the robot. The particles represent pose with respect to themeasurements of the sensors. This allows the robot to avoid storing rawmeasurements of the sensor, and store only the particles 135, which ismemory efficient. For example, a storage device 130 can be adapted tostore the particles 135 and/or the particles of other neighboringrobots. The storage device 130 can be implemented using a hard drive, anoptical drive, a thumb drive, an array of drives, or any combinationsthereof.

In some implementations, the particle filter 131 can update the pose ofthe robot using only the measurements of the sensors of the robot.However, the system 100 also includes a particle tuner 133 configured toupdate the particles 135 using external information, i.e., other and/orin addition to the robot's sensors measurements. Specifically, particletuner 133 is based on recognition that if particles of the robotcorrectly represent the current pose of the robot and particles of theneighboring robot correctly represent the current pose of theneighboring robot, a pair of the particles from each robot shouldcorrectly represent a relative pose of the robot. Such a relative posedetermined by a pair of particles can be compared with a relative posedetermined by other means and the result of the comparison is indicativeof the correctness of the particles in the representation of the currentpose. For example, a larger difference between a relative posedetermined by a pair of particles and a relative pose determined byother means indicates a lower probability that the particles representthe poses of the robot correctly.

For example, in some implementations, the system 100 can optionallyinclude a relative pose estimation component 137 that can use sensorinformation to determine the relative pose between two robots. Thesensor information can have various forms and provide reliableestimation of the relative pose. For example, in one scenario, a facialof a neighboring robot is marked with visible markings, while the robotis equipped with a visual camera to detect the presence of the visiblemarkings, e.g., checkerboard and, measure the relative pose betweenrobots (i.e., relative range, bearing and heading). Additionally, oralternatively, the system 100 can receive relative pose estimation froma neighboring robot.

Some embodiments are based on realization that a particle filter solvesa Bayesian inference problem, thus the multi-robot pose fusion shouldalso follow the principles of Bayesian inference to guarantee theperformance of the particle filter. However, the comparison of particlesof different robots is pairwise, i.e., particles are grouped in pairsand two particles of each pair are compared with each other to update apose of a robot. However, when pairing the particles is deterministic,such a pairing can undermine performance guaranties provided by Bayesianinference.

Some embodiments are based on realization that random pairing ofparticles of different robots during probabilistic multi-robotpositioning can reduce computational complexity to O(K), where K is thenumber of randomly selected pairs of particles while ensuring theperformance guarantees of particle filter. Indeed, random pairing isprobabilistic and follows the principles of Bayesian inference toguarantee performance of the particle filter. In addition, randompairing is also simple, computationally efficient, and suitable forparallel computing.

To that end, a particle tuner is configured to pair an arbitrarilysampled particle of the robot with an arbitrarily sampled particle ofthe neighboring robot, determine a weight of the paired particles inreverse proportion to an error between a relative pose defined by thepaired particles and the relative pose between the robot and theneighboring robot, and update the particles of the robot in accordanceto the weights of corresponding paired particles. As used herein,arbitrarily paired particles are sampled arbitrarily, i.e., notdeterministically. Such an arbitrarily paring can be implemented usingany random and/or a pseudo-random generator configured to select numbersfrom a set of numbers with equal probability, such that any number isequally likely to be selected from the set. In differentimplementations, particles are sampled uniformly randomly ornon-uniformly randomly according to weights of the particle, such as aparticle with a larger weight is more likely to be sampled than aparticle with a smaller weight.

A network interface controller 150 is adapted to connect the system 100through the bus 106 to a network 190. Through the network 190, usingtransceiver 126, the system can transmit the particles of the robot tothe neighboring robot and/or request the neighboring robot to transmitits particles. In addition, the system 100 includes a sensor interface180 to request the measurements from the sensors of the robot and/or todetect rendezvous with the neighboring robot when the robot is inproximity to the neighboring robot to request the neighboring robot totransmit its particles.

In some implementations, a human machine interface 110 within the system100 connects the system to a keyboard 111 and pointing device 112,wherein the pointing device 112 can include a mouse, trackball,touchpad, joy stick, pointing stick, stylus, or touchscreen, amongothers. The system 100 includes an output interface configured to outputthe current pose of the robot. For example, the output interface caninclude a memory to render the pose of the robot and/or variousinterfaces to system benefiting from the estimated pose of the robot.For example, the system 100 can be linked through the bus 106 to adisplay interface 160 adapted to connect the system 100 to a displaydevice 165, wherein the display device 165 can include a computermonitor, camera, television, projector, or mobile device, among others.The system 100 can also be connected to an application interface 170adapted to connect the system to the equipment 128 for performing arobot specific tasks based on position of the robot.

Particle Filter

In various embodiments, the particle filter 131 is configured toestimate the pose of the robot. The following provides a brief overviewof the particle filter (PF)-based positioning algorithm used by someembodiments additionally or alternatively with multi-robot data fusion.

FIG. 2A is an illustration of a pose of a robot in a reference systemused by some embodiments. A pose 210 estimation of a robot 200 in a 2Denvironment is concerned with estimating robot's 2D coordinates (x, y)211 and 212 and orientation θ213 with respect to the coordinate systemassociated with the environment. The 2D coordinates and orientation attime t are collected into a pose vector x_(t)=[x_(t)y_(t)θ_(t)]^(T),where the operator T denotes the vector/matrix transpose.

FIG. 2B is an example of an occupancy grid map used by some embodiments.The knowledge about the environment is represented with an occupancygrid map m∈{0,1}, obtained by dividing the area into N bins, such thatm_(i)=1 in case the ith bin is occupied, or m_(i)=0, otherwise. In thisexample, an unknown area 220 is divided into 8 by 8 bins where a bin iseither occupied 222 or unoccupied 221. For example, multiple consecutivebins that are occupied indicate presence of a wall 223.

In some implementations, at least two types of measurements, i.e.,environmental and motion measurements, are collected by sensors 102-105as the robot travels through the environment. The environmentalmeasurements can be produced by, e.g., a laser scan at time t thatdelivers ranging measurements representing distances from the robot tothe obstacles seen within its field of view. These measurements arecollected into vector z_(t). The ranging measurements z_(t) areprobabilistically modeled with p(z_(t)|x_(t), m), representingprobability of obtaining a realization of z_(t), for a given pose x_(t)and map m. Intuitively, the aim is to give a large probability mass tothe measurements consistent with a given robot pose and map.

The measurements associated with robot motion are collected into vectoru_(t), representing the odometric sensor measurements within the timeinterval (t−1, t]. The odometric sensors can be wheel encoders, in whichcase we talk about true measurements, or control inputs issued to therobot which are treated as measurements for the sake of pose estimation.The robot motion model is probabilistically described withp(x_(t)|x_(t-1), u_(t)), representing a probability of finding a robotat some pose realization x_(t), given its pose x_(t-1) at time t−1, andodometry measurement u_(t). Intuitively, the pose realizations of x_(t)not consistent with the pose at time t−1 and odometry measurementsreceive a relatively small probability mass.

FIG. 3 shows a block diagram of a single robot pose estimation 320 usedby some embodiments. The pose estimation 320 takes as inputs theodometry model and measurements 322, ranging model and measurements 323,and map 321 of the environment, and produces an estimate of robot's pose320.

In some embodiments, the pose estimation 320 is performedprobabilistically by a particle filter 131 using Bayesian inferenceframework. The aim of robot pose estimation within the Bayesianinference framework is to infer the probability distribution of a robotpose x_(t) at time t, given the map and all ranging and odometrymeasurements up to time t. That is, the objective is to find

p(x_(t)|u_(1:t),z_(1:t),m)

p(x_(t)|u₁, . . . , u_(t),z₁, . . . ,z_(t), m).   (1)

In addition, the inference of (1) needs be done sequentially, that is,the belief about robot's pose at time t should be updated from thebelief of its pose at time t−1. This is conceptually done by employingthe Bayes' filter, supplied with the motion p(x_(t)|x_(t-1), u_(t)) andranging model p(z_(t)|x_(t), m). The Bayes' filter boils down to theKalman filter in case of linear and Gaussian motion and ranging models.Otherwise, upon the linearization of those models, the Bayes' filterbecomes the extended Kalman filter. More generally, to avoid modellinearization, the Bayes' filter is implemented by particle filter (PF)according to some embodiments. The PF represents the probabilitydistribution (1) with a certain number of possible pose realizations,called particles. That is the output 330 from pose estimation 320 is aset of pose particles.

FIG. 4A is an illustration of particle cloud in a reference system ofFIG. 2A. A pose of the robot is represented with particles 401, 402,403, 404, 405. Each particle has its own x-coordinate 410, y-coordinate411, and orientation 412 defining the pose. Collectively, the particles401, 402, 403, 404, 405 represent probabilistic distribution of thepose.

FIG. 4B is an illustration of particle cloud in an area according tosome embodiments. Typically, many particles are used to represent thepose of the robot probabilistically. In the example of FIG. 4B, at sometime instant t, where the pose of robot 421 within map 420 isrepresented with a particle cloud 422.

A particle filter can be thought of as approximating the belief ofrobot's pose at time t as

$\begin{matrix}{{{p\left( {{x_{t}u_{1:t}},z_{1:t},m} \right)} \approx {\frac{1}{K}{\sum_{k = 1}^{K}{\delta \left( {x - x_{t,k}} \right)}}}},} & (2)\end{matrix}$

where δ( ) is the Dirac's delta function, K is the overall number ofparticles and X_(t,k) are particles. Although the particle mean canserve as a final point estimate of the robot's pose, their spread (i.e.,variance) suggests the confidence one may have in the pose estimate. Assuch, a fairly confined particles indicate high confidence, althoughthat does not necessarily imply correct pose estimate.

In some implementations, particle filter is initialized with Kparticles, uniformly sampled from the area where the robot is present.Given the set of particles {x_(t-1,k)}_(k=1) ^(K) representing therobot's pose at time t−1 and odometry measurement u_(t) obtained at timet, the robot motion model p(x_(t)|x_(t-1), u_(t)) is used to sample(tentative) particles {x′_(k)}_(k=1) ^(K). Each tentative particlex′_(k) is associated with a weight w_(k) computed from the ranging modeland measurement z_(t),

w_(k)∝p(z_(t)|x′_(k), m)   (3)

and normalized so that Σ_(k=1) ^(K) w_(k)=1. The tentative particles aresampled according to {w_(k)}_(k=1) ^(K) to produce the particle set{x_(t,k)}_(k=1) ^(K), representing the robot's pose at time t.

Robot Rendezvous

In some embodiments, robots occasionally meet and exchange someinformation to aid cooperative pose estimation. In some implementations,the rendezvous occurs randomly or arranged by proper control of therobots. At the rendezvous of two robots, at least one robot has to beenabled to detect the presence of the other robot. In a two-robotscenario, one way to achieve this is to equip one robot with a visualtag and the other one with the RGB camera. Then, a computer visionalgorithm looks for a tag in the RGB camera feed and, in case of arendezvous, detects the presence of the other robot. Other approaches inattaining this requirement are possible. For example, in someimplementations each robot emits a signature ultrasound signal. Thus,when two robots come close to each other, for example are at a distanceof less than 10 meters, they can “hear” each other and detect each otheridentity from the received signature ultrasound signals.

After the robots detect they are in the vicinity of each other, one (orboth robots) measure the relative range r and relative bearing andheading such that heading of one robot with respect to the heading ofthe other robot is φ. In one embodiment, the bearing φ is obtained fromthe RGB camera frames containing the identity tag of the other robot,while the distance r yields from the bearing measurement and rangingscan.

FIG. 5A is a schematic illustrating a rendezvous of two robots in oneembodiment. In this example, a robot A 510 is equipped with acheckerboard 511 which serves as its visual tag. Then, when robot A 510and robot B 512 are in close proximity and in orientation such that thecamera 513 of robot B points toward the checkerboard of robot A, robot Bdetects the presence of robot A and measures their relative pose 515.

For example, in one embodiment, upon detecting robot A, the robot Bperforms relative pose measurements in two steps. First, the location(x,y,z) of the center of the checkerboard pattern is obtained from thepoint cloud created from the depth measurements provided by the RGBDsensor. Then, the relative pose estimation is performed by extractingthe point cloud of the checkerboard corners and estimating the surfacenormal using OpenPCL method.

FIG. 5B is a schematic of a relative pose between two robots used bysome embodiments. To perform information fusion within the Bayesianframework, some embodiments specify a probabilistic model for therelative pose measurement, conditioned on the robots' poses. Formally,this model is captured with p(r, φ|x_(t) ^(A), x_(t) ^(B)), where,referring to FIG. 5B, x_(t) ^(A) 521 and x_(t) ^(B) 522 denote poses oftwo robots at the rendezvous time t. For that purpose, the relativerange r and bearing-heading measurement φ are independent and each has aGaussian distributed error of zero mean and variance σ_(r) ² and σ_(φ)², respectively. That is,

$\begin{matrix}{{{p\left( {r,{\varphi x_{t}^{A}},x_{t}^{B}} \right)} = {{{p\left( {{rx_{t}^{A}},x_{t}^{B}} \right)}{p\left( {{\varphi x_{t}^{A}},x_{t}^{B}} \right)}} = {\left( {{r;d_{t}},\sigma_{r}^{2}} \right)\left( {{\varphi;\rho_{t}},\sigma_{\varphi}^{2}} \right)}}},} & (4)\end{matrix}$

where

(x; μ, σ²)=1/√{square root over (2πσ²)}exp(−(x−μ)²/2σ²) is Gaussiandistributed variable x, of mean μ and variance σ², while d 523 and ρ 524are the relative range and bearing-heading corresponding to the posesx_(t) ^(A) and x_(t) ^(B). In general, the variances σ_(r) ² and σ_(φ) ²can be calibrated from the measured data, or assessed based on theaccuracy of the measurement method and resolution of the map m. Asskilled artisan would recognize, the information fusion described belowis not restricted by the choice of p(r, φ|x_(t) ^(A), x_(t) ^(B)).

Particle Tuner

FIG. 6A is a principle block diagram of a cooperative localizationpipeline used by some embodiments. Initially, a robot is on its own,moves through the environment and executes a single robot positioning601 using particle filter 131. When this robot gets in close proximityof some other robot, one or both robots perform robot detection 605. Therobot detection results in each robot's awareness that the two robotsare close to each other and one or both robots measure relative posebetween them 606, e.g., using pose estimation component 137. In caseonly one robot measures this relative pose, it may send the relativepose measurement to the other robot. Upon this stage, robots exchangetheir pose particles. Each robot then executes cooperative positioning600, which fuses its own pose particles obtained from 601, poseparticles of the other robot 610 and relative pose measurement 606. Thecooperative positioning 600 performed by a robot results in updated poseparticles 615 corresponding to that robot, which are returned into thesingle-robot positioning 601. From there on, each robot is again on itsown and continues running the single robot positioning algorithm untilit meets other robot(s).

Going into more details, two robots A and B meet at time t and exchangetheir pose particles. In addition, the robot that measures relative posebetween robots sends the measurement to the other robot. One embodimentdiscloses information fusion algorithm with respect to robot A. However,the equivalent fusion can be performed by the robot B.

FIG. 6B is a principle block diagram of information fusion performed bya particle tuner 133 according to some embodiments. The set of particlesrepresenting pose of robot A at time t 621, the set of particlesrepresenting pose of robot B at time t and received from robot B 622 arefused together with relative pose measurement(s) 606 according to ouralgorithm implemented in 600. The output of this block 615 is theresulting set of updated particles representing pose of robot A uponrobot's rendezvous.

Assuming, without loss of generality, the robots meet for the firsttime, all ranging and odometric measurements made by robot A up unittime instant t are collectively denoted as

_(t) ^(A)={u_(1:t) ^(A), z_(1:t) ^(A)}. The pose of robot A at time t,described with p(x_(t) ^(A)|

_(t) ^(A), m), is essentially the prior distribution about robot A'spose at the rendezvous time instant t.

Robot A receives from robot B particles Z_(t) ^(B)={x_(t,k) ^(B)}_(k=1)^(K) which robot A treats as

$\begin{matrix}{{p\left( {x_{t}^{B}X_{t}^{B}} \right)} = {\frac{1}{K}{\sum_{k = 1}^{K}{\delta \left( {x_{t}^{B} - x_{t,k}^{B}} \right)}}}} & (5)\end{matrix}$

Notably, conditioning on ranging and odometric measurements collected byrobot B up until time t is avoided in (5) because all what robot A hasaccess to are robot B's particles, which it then uses to build up aprobabilistic representation of robot B's pose. In addition to robot B'sparticles, robot A also has access to the measurements of the relativerange r and bearing-heading φ, either directly from its ownmeasurements, or indirectly by receiving them from robot B.

After robot A receives robot B's particles and obtains measurements of rand φ, robot A fuses them with the current estimate of its pose x_(t)^(A). Formally, this is done by means of the Bayesian inference whichaims to compute the posterior of the pose x_(t) ^(A), conditioned on allinformation available to robot A. Subsuming the time index t in allexpressions as well as the explicit conditioning on the map m to avoidnotation clutter, the posterior of robot A's pose is given by

$\begin{matrix}{{p\left( {{x^{A}^{A}},r,\varphi,X^{B}} \right)} = {{\int{{p\left( {x^{A},{x^{B}^{A}},r,\varphi,X^{B}} \right)}{dx}^{B}}}\overset{(1)}{=}{{\eta {\int{{p\left( {r,{\varphi x^{A}},x^{B}} \right)}{p\left( {x^{A},{x^{B}^{A}},X^{B}} \right)}{dx}^{B}}}} = {\eta {\int{{p\left( {r,{\varphi x^{A}},x^{B}} \right)}{p\left( {x^{A}^{A}} \right)}{p\left( {x^{B}X^{B}} \right)}{dx}^{B}}}}}}} & (6)\end{matrix}$

where η

p(r, φ|

^(A), X^(B)) does not depend on x^(B) and

follows from the Bayes' theorem and the conditional independence of rand φ on D^(A) and X, when conditioned on x^(A) and x^(B). Substituting(5) into (6) yields

$\begin{matrix}{{p\left( {{x^{A}^{A}},r,\varphi,X} \right)} = {\frac{\eta}{K}{p\left( {x^{A}^{A}} \right)}{\sum_{k = 1}^{K}{p\left( {r,{\varphi x^{A}},x_{k}^{B}} \right)}}}} & (7)\end{matrix}$

In general, robot A's pose is updated using (7) given its posedistribution p(x^(A)|

^(A)) prior to the rendezvous is known. We use importance sampling todraw samples that represent the posterior of robot A's pose upon therendezvous. According to the importance sampling terminology, theposterior (7) is the target distribution. The proposal distribution usedto draw samples from is p(x^(A)|

^(A)). Thus, the importance sampling starts with

x_(l) ^(A)˜p(x^(A)|

^(A)), l=1, . . . , L.   (8)

Given that robot A's prior p(x^(A)|

D^(A)) is represented with particles X^(A), the particles in (8) areeffectively obtained by sampling uniformly at random from X^(A). Theweights associated with the resulting particles are computed from theratio between the target and proposal distributions

$\begin{matrix}{w_{l} = {\frac{p\left( {{x_{l}^{A}^{A}},r,\varphi,X} \right)}{p\left( {x_{l}^{A}^{A}} \right)} \propto {\sum_{k = 1}^{K}{p\left( {r,{\varphi x_{l}^{A}},x_{k}^{B}} \right)}}}} & (9)\end{matrix}$

and normalized so that Σ_(l=1) ^(L) w_(l)=1. Finally, the set ofparticles {x_(l) ^(A)}l=1 ^(L) is updated 615, e.g., resampled accordingto {w_(l)}_(l=1) ^(L) to yield the final set of particles with uniformweights, which represents robot A's pose posterior after the rendezvous.Alternatively, the updated weights of the particles can be preserved toproduce non-uniformly sampled particles.

FIG. 7 is a pseudo-code of the cooperative positioning used by oneembodiment. The embodiment is based on recognition that thecomputational bottleneck of the described method arises from (9), whichrequires K evaluations of the relative pose probability distribution foreach particle x_(l) ^(A) (provided no repetitions). To reduce thecomplexity, the embodiment replaces the sum in (9) with a singleevaluation of the relative pose distribution at the considered x_(l)^(A) and a uniformly at random sampled particle from X^(B). This resultsin particle update scheme of linear complexity in the number of robotA's particles. The output from the algorithm is the set of particles{tilde over (X)}^(A) representing robot A's pose posterior upon fusingthe information received from robot B as well as the relative posemeasurements. All computations for the pose posterior update are donelocally on robot A's platform.

Analogously, the same information fusion is used by particle tuner ofrobot B to update robot B's posterior upon receiving robot A's particlesrepresenting its pose prior to the rendezvous at time t, as well as therelative pose measurements. The information fusion is executed locallyon robot B's platform by the particle tuner of robot B and the output isthe set of particles {tilde over (X)}^(B) representing robot B's poseposterior upon the rendezvous.

After the rendezvous, each robot supplies its particle filter with theupdated particle set {tilde over (X)}^(A)/{tilde over (X)}^(B) andcontinues moving through the area on its own in a single-robot modeuntil the next rendezvous with the same or some other robot. Someembodiments exercise a caution though so that a robot does not updateits pose particles based on multiple rendezvous with the same robot in ashort time interval. This could effectively lead to fusing the same orsimilar information multiple times and result in producingover-confident and possibly wrong estimates. For example, in someembodiments the data fusion is performed, e.g., a robot A requests therobot B to transmit its particles upon detecting the rendezvous, onlywhen a distance between the rendezvous and a previous rendezvous ofrobots A and B is above a threshold. For example, in differentembodiments, the distance is one or combination of a time passed sincethe previous rendezvous, and a distance covered by the robot since theprevious rendezvous.

Notably, if robot B's pose is known and relative pose measurements arecorrect, robot A's pose immediately follows from transforming robot B'spose according to the relative pose measurements. Thus, one embodimentconsiders the case where robot B's particles prior to the rendezvous areconfined within a small space around robot B's true pose, while robotA's particles are spread throughout the area. Thus, each particle x_(l)^(B) sampled from X^(B) is within such a confined space, while auniformly sampled particle x_(l) ^(A) is anywhere in the area.Consequently, the weight w_(l) computed for x_(l) ^(A) is relativelylarge if x_(l) ^(A) and x_(l) ^(B) are in accordance with the relativepose measurements, and relatively small otherwise. Therefore, assumingrelative pose measurements of descent quality, all particles x_(l) ^(A)from

which are at about robot A's true pose survive the resampling step andpopulate the final output {tilde over (X)}^(A), which is the desiredoutcome.

Exemplar Implementation of Particle Tuner

FIG. 8A is a block diagram of a method for computing a weighted particlepair according to some embodiments. The method generates a single poseparticle pair and its weight. The method is implemented by a particletuner of robot A. The method samples at random 811 a pose particle fromthe set of pose particles 621 corresponding to robot A's poseimmediately prior to the rendezvous. Similarly, a pose particle from theset of pose particles 622 corresponding to robot B's pose immediatelyprior to the rendezvous is also sampled at random 812. The blocks 811and 812 thus yield a pair of pose particles. The pair of particles isweighted 815 according to the relative pose measurement 606 and relativepose model, for example as suggested by (9). Therefore, the wholeprocess 800 outputs a weighted pair of pose particles 820.

In one embodiment, the particle tuner samples the particles of the robotuniformly randomly, such that any particle from a set of particles ofeach robot is equally likely to be sampled, i.e., selected from the set.This embodiment is advantageous when all particles have equal weight. Inalternative embodiment, the particle tuner samples the particles of therobot non-uniformly randomly according to weights of the particles, sothat a particle with a larger weight is more likely to be sampled than aparticle with a smaller weight. This embodiment is advantageous whendifferent particles can have different weight.

FIG. 8B is a block diagram of a method used by some embodiments forupdating particles based on a weighted pair of pose particles generatedas shown in FIG. 8A. For example, a number of weighted pairs of poseparticles are generated 800 in parallel. The parallel implementationyields overall a quick update of pose particles at robots' rendezvous.Each parallel branch outputs one weighted pair of pose particles. Theoutputs of all parallel branches are collected and their weights arenormalized such that they sum up to one 830. To that end, in someembodiments, the particle tuner is configured to pair and weight thepaired particles in parallel. For example, the processor is a parallelprocessor having multiple CPUs.

In some implementations, the normalized weights of the particles arepreserved to result in the weighted set of particles. Additionally, oralternatively, in some embodiments the weighted particles are resampledaccording to their weights to result in equally weighted set ofparticles. For example, the pose particle pairs are resampled 835according to the normalized weights such that the pairs with largerweight have more chance to be sampled. The result of this step is a setof pose particle pairs. If the method is executed on robot A, the poseparticles corresponding to robot A in the pairs of pose particles areextracted and their set is the set of updated pose particles 615.Similarly, pose particles corresponding to robot B are extracted fromthe set of pose particle pairs and their set is the set of updated poseparticles 615.

Pseudo-Random Sampling

Various embodiments embed random sampling with repetitions of poseparticles according to some discrete distribution. Assuming L particles,denote this distribution with vector z such that its l-th entry z_(l)denotes the probability of selecting the l-th particle. As used herein,Σ_(l=1) ^(L) z_(l)=1 and sampling with repetitions means that the sameparticle can be sampled multiple times. One example of distribution zused in the disclosed methods is uniform distribution, where z_(l)=1/L,l=1, . . . ,L, which is used in generating pairs of pose particles 811,812. In another example, z, z_(l)=w_(l)/Σ_(l=1) ^(L) w_(l), and is usedfor resampling pairs of pose particles 835.

FIG. 9A is a block diagram of pseudo-random particle sampling used bysome embodiments to implement particle sampling for a given discretedistribution z. Without loss of generality, in example of FIG. 9A L=4such that the desired discrete distribution 903 has entries z₁, z₂, z₃,z₄. The pseudo-random number generator 901 uniformly at random samples anumber between 0 and 1 such that each number in that range is equallylikely to be selected. An index of a sampled particle is determined 905based on the desired discrete distribution 903 and the pseudo-randomnumber 902. In doing so, the range between 0 and 1 is divided accordingto the desired discrete distribution into L=4 segments of lengths z₁,z₂, z₃ and z₄, and the sampled index is the index of the segment wherethe pseudo-random number 902 lands 907. As shown in FIG. 9A, thepseudo-random number 902 is between z₁+z₂ and z₁+z₂+z₃ and,consequently, the output 908 from 905 is index 3. In general, the output908 is an integer between 1 and L that goes onto pose particle look-up909. The particle with such an index is delivered as a sampled poseparticle 910. The described particle sampling implementation is used in811 and 812 of FIG. 8A with z_(l)=1/L, l=1, . . . , L. Also, thedescribed particle sampling implementation is used in resampling 835 ofFIG. 8B where multiple particles are sampled with z_(l)=w_(l)/Σ_(l=1)^(L) w_(l) from the collection of weighted particle pairs 830. Thenumber of times the particle sampling routine from FIG. 9A is invoked in835 is equal to the desired number of updated particles.

Accordingly, some embodiments use a random number generator for samplinga pose particle. In general, the output of a random number generatorshould be a purely random number between 0 and 1, where each number fromthis range is equally likely to be sampled. Since the implementation ofthe random number generator in a processor is deterministic, the outputfrom this block cannot be purely random. In fact, the output from therandom number generator is deterministic. However, the random numbergenerator is designed such that in a long run, the sequence it producesresembles a sequence of random numbers. For those reasons, the randomnumber generator is commonly referred to as a pseudo-random numbergenerator, e.g., the pseudo-random number generator 901.

As used herein, by “resembles” mean that the pseudo-random numbergenerator 901 generated sequence approximately satisfies two propertiesthat a purely random and infinitely long sequence coining out from arandom number generator would satisfy. The first property is related tohaving the generated numbers abide with uniform distribution, meaningthat the histogram of the generated numbers is flat. The second propertyis related to having the generated numbers be unrelated to each other,which translates to having the normalized autocorrelation of thesequence be delta function (equal to one at zero lag and zero at allnon-zero lags).

FIG. 9B is a block diagram of pseudo-random number generation used byone embodiment. The pseudo-random number generator 901 includes a linearcongruential generator (LCG) 922 which generates a sequence ofpseudo-random integers according to

y _(n) =ay _(n-1) +bmodm   (10)

where y_(n) is the n-th number in the sequence, a, b and m are fixedscalars, while mod denotes a modulus operation which yields theremainder of the division of ay_(n-1)+b with m. Thus, y_(n) can be anyinteger between 0 and m −1. Commonly, m is the largest integer than canbe stored in the processor.

The first entry in the sequence, y₁, is generated based on y₀ which isprovided by the pre-fixed seed 921. For n>1, y_(n) is generated based ony_(n-1) such that y_(n-1) needs to be stored and fed back 923. Eachentry in the sequence of pseudo-random integers 924 is divided by m 925to yield a sequence 902 of pseudo-random numbers between 0 and 1. Othermethods may be used to generate a sequence of pseudo-random numbers. Forexample, more outputs y_(n-k), k>0 can be fed back to generate y_(n)using congruence relation.

Effects of Some Embodiments

Other methods for information fusion update pose particles of a robotbased on pose particles of two robots prior to their rendezvous andrelative pose measurement. As such, one method uses density trees toestimate robot's pose from its particles before fusion. In comparison tothat method, the methods disclosed herein do not need to employ densitytrees and hence does not incur additional computational cost. Othermethod considers all pairs of pose particles originating from differentrobots and each pair is weighted based on how much its pose particlesagree with the relative pose measurement. Assuming particle cloud ofeach robot contains L particles, the overall computational cost ofcomputing weights of all possible particle pairs is of the order L². Incomparison, the methods disclosed herein generate L pairs of particlesso that the computational complexity of pose particle update is of theorder L. In yet another method, pose particles of one robot areclustered into S clusters. Then, all pairwise combinations between Sparticles representing each of S clusters and L pose particles from theother robot are formed and their weights are computed based on theagreement with the relative pose measurement. Therefore, the complexityof weight computation in this method is thus of the order KS.

Aside from lower computational complexity, the methods disclosed hereinhave an additional benefit with respect to other methods. In particular,since pairs of particles are independent of each other, generation andweight computation of particle pairs can be done in parallel, yieldingto a possibly significant saving in time needed to update pose particlesupon the rendezvous. In other words, the amount of time needed togenerate and compute all particle pairs in our method is equal to theamount of time needed to generate and compute the weight of a singleparticle pair. In comparison, the method with clusters requires KS timeslonger period to just compute weights of particle pairs, plus additionaltime period to perform clustering.

The methods disclosed herein are derived by meretriciously abiding withthe statistical inference principles and are optimal in the Bayesianinference framework, the above discussed benefits do not come at a costof deteriorated performance. Instead, performance guarantees of ourmethod stein from its optimality in the Bayesian sense and are the sameas for a conventional particle filter.

Nonuniform Particle Weights

Some implementations of various embodiments assume that pose particlesof both robots immediately prior to their rendezvous are with uniformweights. It means that each particle in a set of pose particlescontaining L particles has weight 1/L. Also, the described methodoutputs a set of updated pose particle upon the rendezvous afterresampling 835, meaning that the updated pose particles have uniformweight. Overall, the input and output pose particles are assumed to haveuniform weight.

Some other implementations use other options for pose particle weights.As such, referring to FIG. 8B, one embodiment of the disclosed methodmay skip resampling pose particle pairs 835 and, instead, directlyoutput pose particles corresponding to the considered robot withnormalized weights. Similarly, the set of pose particles from robot A621 and/or robot B 622 may contain weighted particles. If so, it iscommon that the weights are normalized so that they sum up to one. Ifnot, they should be first normalized. Then, referring to FIG. 8A, therandom sampling of pose particles 811 and/or 812 is not uniform, butaccording to particle weights such that the particles carrying largerweight are more likely to be selected.

Multiple Measurements of Relative Pose

In some embodiments, robots measure their relative pose when they meet.The relative pose measurement may be a single measurement made by onlyone robot and communicated to the other. Alternatively, each robot maymeasure the relative pose and share the measurements with the otherrobot. As yet another alternative and more general case, each robot mayperform multiple relative pose measurements and exchange them with theother robot. As a result, each robot may have M relative posemeasurements r₁, r₂, . . . , r_(M) and φ₁, φ₂, . . . , φ_(M). In thatcase, and assuming the robots do not move while M measurements have beentaken, the weight w_(l) is computed as

w_(l)∝p(r₁, r₂, . . . , r_(M), φ₁, φ₂, . . . , φ_(M)|x_(l) ^(A), x_(l)^(B))   (11)

Assuming multiple pose measurements are conditionally independent forgiven robots' poses x_(l) ^(A) and x_(l) ^(B), the weight w_(l) is givenby

w∝Π_(m=1) ^(M)p(r_(m), φ_(m)|x_(l) ^(A), x_(l) ^(B))   (12)

where p(r_(m), φ_(m)|x_(l) ^(A), x_(l) ^(B)) is evaluated from therelative pose measurement model such as one in (4).

Multiple Rendezvous of Two Robots

Two robots continue on their own upon rendezvous following higher-levelinstructions depending on the task they are executing. Given that theymay meet again, a natural question arises as to how to update poseparticles at their following rendezvous. In general, the same methodscan apply. However, if two robots meet two or more times in a relativelyshort time interval, using the described method may lead to fusing thesame information multiple times. The resulting pose particles thenshrink more than they should, resulting in over-confident poseestimates. To ensure this does not happen, in some implementations therobots do not perform information fusion unless one or both havetraversed at least a certain, application-dependent, distance. Byallowing robots to exchange and fuse information only after traversing acertain distance, we ensure that the amount of new information therobots have collected since their last rendezvous is large enough toavoid obtaining severely over-confident pose estimates.

Rendezvous of Multiple Robots

The disclosed methods are scalable to cooperative localization of morethan two robots. Namely, suppose robot A first meets robot B, moves abit and then meets robot C. In such a scenario, robot A first updatesits pose particles based on the information it receives from robot B andperforms single robot positioning until it meets robot C. Then robot Aupdates its most recent pose particles using the information it receivesfrom robot C.

Similarly, assume robots A, B and C meet at the same time. In such acase, robot A first updates its pose particles based on the informationit receives from one of the robots, for example, robot B. Then, robot Aupdates its most recent pose particles based on the information itreceives from the other robot, for example robot C. Other robots proceedwith updating their pose particles in a similar way.

FIG. 10 shows a block diagram of a positioning system 1000 of a robotaccording to some embodiments. The system 1000 can be implementedinternal to the robot A and/or B. Additionally or alternatively, thesystem 1000 can be communicatively connected to the robot A and/or B.

The system 1000 can include one or combination of a camera 1010, aninertial measurement unit (IMU) 1030, a processor 1050, a memory 1060, atransceiver 1070, and a display/screen 1080, which can be operativelycoupled to other components through connections 1020. The connections1020 can comprise buses, lines, fibers, links or combination thereof.

The transceiver 1070 can, for example, include a transmitter enabled totransmit one or more signals over one or more types of wirelesscommunication networks and a receiver to receive one or more signalstransmitted over the one or more types of wireless communicationnetworks. The transceiver 1070 can permit communication with wirelessnetworks based on a variety of technologies such as, but not limited to,femtocells, Wi-Fi networks or Wireless Local Area Networks (WLANs),which may be based on the IEEE 802.11 family of standards, WirelessPersonal Area Networks (WPANS) such Bluetooth, Near Field Communication(NFC), networks based on the IEEE 802.15x family of standards, and/orWireless Wide Area Networks (WWANs) such as LTE, WiMAX, etc. The system400 can also include one or more ports for communicating over wirednetworks.

In some embodiments, the system 1000 can comprise image sensors such asCCD or CMOS sensors, lasers and/or camera 1010, which are hereinafterreferred to as “sensor 1010”. For example, the sensor 1010 can convertan optical image into an electronic or digital image and can sendacquired images to processor 1050. Additionally, or alternatively, thesensor 1010 can sense the light reflected from a target object in ascene and submit the intensities of the captured light to the processor1050.

For example, the sensor 1010 can include color or grayscale cameras,which provide “color information.” The term “color information” as usedherein refers to color and/or grayscale information. In general, as usedherein, a color image or color information can be viewed as comprising 1to N channels, where N is some integer dependent on the color spacebeing used to store the image. For example, an RGB image comprises threechannels, with one channel each for Red, Blue and Green information.

For example, the sensor 1010 can include a depth sensor for providing“depth information.” The depth information can be acquired in a varietyof ways using depth sensors. The term “depth sensor” is used to refer tofunctional units that may be used to obtain depth informationindependently and/or in conjunction with some other cameras. Forexample, in some embodiments, the depth sensor and the optical cameracan be part of the sensor 1010. For example, in some embodiments, thesensor 1010 includes RGBD cameras, which may capture per-pixel depth (D)information when the depth sensor is enabled, in addition to color (RGB)images.

As another example, in some embodiments, the sensor 1010 can include a3D Time Of Flight (3DTOF) camera. In embodiments with 3DTOF camera, thedepth sensor can take the form of a strobe light coupled to the 3DTOFcamera, which can illuminate objects in a scene and reflected light canbe captured by a CCD/CMOS sensor in the sensor 1010. Depth informationcan be obtained by measuring the time that the light pulses take totravel to the objects and back to the sensor.

As a further example, the depth sensor can take the form of a lightsource coupled to the sensor 1010. In one embodiment, the light sourceprojects a structured or textured light pattern, which can include oneor more narrow bands of light, onto objects in a scene. Depthinformation is obtained by exploiting geometrical distortions of theprojected pattern caused by the surface shape of the object. Oneembodiment determines depth information from stereo sensors such as acombination of an infra-red structured light projector and an infra-redcamera registered to a RGB camera.

In some embodiments, the sensor 1010 includes stereoscopic cameras. Forexample, a depth sensor may form part of a passive stereo vision sensor,which may use two or more cameras to obtain depth information for ascene. The pixel coordinates of points common to both cameras in acaptured scene may be used along with camera pose information and/ortriangulation techniques to obtain per-pixel depth information.

In some embodiments, the system 1000 can be operatively connected tomultiple sensors 1010, such as dual front cameras and/or a front andrear-facing cameras, which may also incorporate various sensors. In someembodiments, the sensors 1010 can capture both still and video images.In some embodiments, the sensor 1010 can include RGBD or stereoscopicvideo cameras capable of capturing images at, e.g., 30 frames per second(fps). In one embodiment, images captured by the sensor 1010 can be in araw uncompressed format and can be compressed prior to being processedand/or stored in memory 1060. In some embodiments, image compression canbe performed by the processor 1050 using lossless or lossy compressiontechniques.

In some embodiments, the processor 1050 can also receive input from IMU1030. In other embodiments, the IMU 1030 can comprise 3-axisaccelerometer(s), 3-axis gyroscope(s), and/or magnetometer(s). The IMU1030 can provide velocity, orientation, and/or other position relatedinformation to the processor 1050. In some embodiments, the IMU 1030 canoutput measured information in synchronization with the capture of eachimage frame by the sensor 1010. In some embodiments, the output of theIMU 1030 is used in part by the processor 1050 to fuse the sensormeasurements and/or to further process the fused measurements.

The system 1000 can also include a screen or display 1080 renderingimages, such as color and/or depth images. In some embodiments, thedisplay 1080 can be used to display live images captured by the sensor1010, fused images, augmented reality (AR) images, graphical userinterfaces (GUIs), and other program outputs. In some embodiments, thedisplay 1080 can include and/or be housed with a touchscreen to permitusers to input data via some combination of virtual keyboards, icons,menus, or other GUIs, user gestures and/or input devices such as styliand other writing implements. In some embodiments, the display 1080 canbe implemented using a liquid crystal display (LCD) display or a lightemitting diode (LED) display, such as an organic LED (OLED) display. Inother embodiments, the display 480 can be a wearable display. In someembodiments, the result of the fusion can be rendered on the display1080 or submitted to different applications that can be internal orexternal to the system 1000.

Exemplary system 1000 can also be modified in various ways in a mannerconsistent with the disclosure, such as, by adding, combining, oromitting one or more of the functional blocks shown. For example, insome configurations, the system 1000 does not include the IMU 1030 orthe transceiver 1070. Further, in certain example implementations, thesystem 1000 include a variety of other sensors (not shown) such as anambient light sensor, microphones, acoustic sensors, ultrasonic sensors,laser range finders, etc. In some embodiments, portions of the system400 take the form of one or more chipsets, and/or the like.

The processor 1050 can be implemented using a combination of hardware,firmware, and software. The processor 1050 can represent one or morecircuits configurable to perform at least a portion of a computingprocedure or process related to sensor fusion and/or methods for furtherprocessing the fused measurements. The processor 1050 retrievesinstructions and/or data from memory 1060. The processor 1050 can beimplemented using one or more application specific integrated circuits(ASICs), central and/or graphical processing units (CPUs and/or GPUs),digital signal processors (DSPs), digital signal processing devices(DSPDs), programmable logic devices (PLDs), field programmable gatearrays (FPGAs), controllers, micro-controllers, microprocessors,embedded processor cores, electronic devices, other electronic unitsdesigned to perform the functions described herein, or a combinationthereof.

The memory 1060 can be implemented within the processor 1050 and/orexternal to the processor 1050. As used herein the term “memory” refersto any type of long term, short term, volatile, nonvolatile, or othermemory and is not to be limited to any particular type of memory ornumber of memories, or type of physical media upon which memory isstored. In some embodiments, the memory 1060 holds program codes thatfacilitate the multi-robot probabilistic positioning 1055.

For example, the memory 1060 can store the measurements of the sensors,such as still images, depth information, video frames, program results,as well as data provided by the IMU 1030 and other sensors. The memory1060 can store a memory storing a geometry of the robot, a map of thespace, a kinematic model of the robot, and a dynamic model of the robot.In general, the memory 1060 can represent any data storage mechanism.The memory 1060 can include, for example, a primary memory and/or asecondary memory. The primary memory can include, for example, a randomaccess memory, read only memory, etc. While illustrated in FIG. 4 asbeing separate from the processors 1050, it should be understood thatall or part of a primary memory can be provided within or otherwiseco-located and/or coupled to the processors 1050.

Secondary memory can include, for example, the same or similar type ofmemory as primary memory and/or one or more data storage devices orsystems, such as, for example, flash/USB memory drives, memory carddrives, disk drives, optical disc drives, tape drives, solid statedrives, hybrid drives etc. In certain implementations, secondary memorycan be operatively receptive of, or otherwise configurable to anon-transitory computer-readable medium in a removable media drive (notshown). In some embodiments, the non-transitory computer readable mediumforms part of the memory 1060 and/or the processor 1050.

The above-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments may beimplemented using hardware, software or a combination thereof. Whenimplemented in software, the software code can be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers. Such processorsmay be implemented as integrated circuits, with one or more processorsin an integrated circuit component. Though, a processor may beimplemented using circuitry in any suitable format.

Also, the embodiments of the invention may be embodied as a method, ofwhich an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

Use of ordinal terms such as “first,” “second,” in the claims to modifya claim element does not by itself connote any priority, precedence, ororder of one claim element over another or the temporal order in whichacts of a method are performed, but are used merely as labels todistinguish one claim element having a certain name from another elementhaving a same name (but for use of the ordinal term) to distinguish theclaim elements.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention.

Therefore, it is the object of the appended claims to cover all suchvariations and modifications as come within the true spirit and scope ofthe invention.

We claim:
 1. A system for estimating a pose of a robot, wherein the poseincludes one or combination of a location of the robot and anorientation of the robot, comprising: an input interface configured toreceive data indicative of a value of a relative pose between a currentpose of the robot and a current pose of a neighboring robot, andindicative of values of particles of the neighboring robot, eachparticle of the neighboring robot defines a probability of a value ofthe current pose of the neighboring robot; a memory configured to storevalues of particles of the robot, each particle of the robot defines aprobability of a value of the current pose of the robot, and storeexecutable components including a particle filter configured to trackthe pose of the robot using a set of particles, each particle defines aprobability of a value of the current pose of the robot; a particletuner configured to pair an arbitrarily sampled particle of the robotwith an arbitrarily sampled particle of the neighboring robot, determinea weight of the paired particles in reverse proportion to an errorbetween a relative pose defined by the paired particles and the relativepose between the robot and the neighboring robot, and update theparticles of the robot in accordance to the weights of correspondingpaired particles; a processor configured to track, in response to achange of the pose of the robot, the pose of the robot using theparticle filter, and to update, in response to receiving the data, theparticles of the particle filter using the particle turner; and anoutput interface configured to output the current pose of the robot. 2.The system of claim 1, wherein the particle tuner randomly samples theparticles of the robot to pair the arbitrarily sampled particles.
 3. Thesystem of claim 2, wherein the particle tuner samples the particles ofthe robot uniformly randomly.
 4. The system of claim 2, wherein theparticle tuner samples the particles of the robot non-uniformly randomlyaccording to weights of the particles, such as a particle with a largerweight is more likely to be sampled than a particle with a smallerweight.
 5. The system of claim 1, wherein the particle tuner, to updatethe particles of the robot, is configured to resample the particlesaccording to their weights to produce a set of particles representingthe pose of the robot with equal weights.
 6. The system of claim 1,wherein the particle tuner, to update the particles of the robot, isconfigured to normalize weights of the particles to produce a set ofparticles representing the pose of the robot with different weights. 7.The system of claim 1, further comprising: a pseudo-random generatorconfigured to select numbers from a set of numbers with equalprobability, such that any number is equally likely to be selected fromthe set, wherein the particle tuner is configured to select a numberusing the pseudo-random generator and select one or combination of aparticle of the robot and a particle of the neighboring robot based onthe number to form the paired particles.
 8. The system of claim 1,wherein the processor requests the neighboring robot to transmit itsparticles upon detecting the rendezvous with the neighboring robot whena distance between the rendezvous and a previous rendezvous is above athreshold.
 9. The system of claim 8, wherein the distance is one orcombination of a time passed since the previous rendezvous, and adistance covered by the robot since the previous rendezvous.
 10. Thesystem of claim 1, wherein the particle tuner is configured to pair andweight the paired particles in parallel.
 11. The system of claim 10,wherein the processor is a parallel processor.
 12. The robot forperforming a task, comprising: a motor configured to change the pose ofthe robot; the system of claim 1 configured to track the pose of therobot; a receiver configured to receive the particles of neighboringrobot; a transmitter configured to transmit the particles of the robotto the neighboring robot; and at least on sensor configured to detectrendezvous with the neighboring robot when the robot is in proximity tothe neighboring robot and provide environmental and odometrymeasurements to the particle filter for tracking the pose of the robot.13. A method for estimating a pose of a robot, wherein the pose includesone or combination of a location of the robot and an orientation of therobot, wherein the method uses a processor coupled with storedinstructions implementing the method, wherein the instructions, whenexecuted by the processor carry out steps of the method, comprising:receiving data indicative of a value of a relative pose between acurrent pose of the robot and a current pose of a neighboring robot, andindicative of values of particles of the neighboring robot, eachparticle of the neighboring robot defines a probability of a value ofthe current pose of the neighboring robot; tracking the pose of therobot using a set of particles, each particle defines a probability of avalue of the current pose of the robot; pairing an arbitrarily sampledparticle of the robot with an arbitrarily sampled particle of theneighboring robot; determining a weight of the paired particles inreverse proportion to an error between a relative pose defined by thepaired particles and the relative pose between the robot and theneighboring robot; and updating the particles of the robot in accordanceto the weights of corresponding paired particles.
 14. The method ofclaim 1, wherein the particles of the robot are randomly sampled to pairthe arbitrarily sampled particles.
 15. The method of claim 14, whereinthe particles of the robot are sampled uniformly randomly.
 16. Themethod of claim 14, wherein the particles of the robot are samplednon-uniformly randomly according to weights of the particles, such as aparticle with a larger weight is more likely to be sampled than aparticle with a smaller weight.
 17. The method of claim 13, furthercomprising: resampling the particles according to their weights toproduce a set of particles representing the pose of the robot with equalweights.
 18. The method of claim 13, further comprising: normalizingweights of the particles to produce a set of particles representing thepose of the robot with different weights.
 19. The method of claim 13,further comprising: requesting the neighboring robot to transmit itsparticles upon detecting the rendezvous with the neighboring robot whena distance between the rendezvous and a previous rendezvous is above athreshold, wherein the distance is one or combination of a time passedsince the previous rendezvous, and a distance covered by the robot sincethe previous rendezvous.
 20. A non-transitory computer readable storagemedium embodied thereon a program executable by a processor forperforming a method, the method comprising: receiving data indicative ofa value of a relative pose between a current pose of the robot and acurrent pose of a neighboring robot, and indicative of values ofparticles of the neighboring robot, each particle of the neighboringrobot defines a probability of a value of the current pose of theneighboring robot; tracking the pose of the robot using a set ofparticles, each particle defines a probability of a value of the currentpose of the robot; pairing an arbitrarily sampled particle of the robotwith an arbitrarily sampled particle of the neighboring robot;determining a weight of the paired particles in reverse proportion to anerror between a relative pose defined by the paired particles and therelative pose between the robot and the neighboring robot; and updatingthe particles of the robot in accordance to the weights of correspondingpaired particles.